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Chengchun Hao's Publications

PUBLICATIONS

My papers in ResearchGate, arXiv, MathSciNet, Google Scholar, ORCID

Preprints

  1. Jie Fu, Chengchun Hao and Wei Zhang;
    On the splash singularity for a 3d free-boundary incompressible viscoelastic fluid model NEW
    In preparation, 2025.
  2. Chengchun Hao, Tao Luo and Siqi Yang;
    Classification of finite-time blow-up of strong solutions to the incompressible free boundary Euler equations with surface tension NEW
    In preparation, 2025.
  3. Wei Zhang, Jie Fu, Chengchun Hao and Siqi Yang;
    Global well-posedness of the free boundary problem for incompressible viscous resistive MHD in critical Besov spaces
    Submitted, 2024.

    Accepted Papers


    Published Journal Articles

    ■ Free boundary problems in fluid dynamics equations

    ♣ MHD equations
  1. Chengchun Hao and Siqi Yang;
    A priori estimates and a blow-up criterion for the incompressible ideal MHD equations with surface tension and a closed free surface NEW
    Nonlinearity, 38(7): 075009 (47pp), 2025.
  2. Chengchun Hao and Siqi Yang;
    On a regularity criterion for free boundary incompressible ideal MHD with surface tension NEW
    To appear, Communications in Information and Systems, 25: 18pp, 2025.
  3. Chengchun Hao and Siqi Yang;
    Splash singularity for the free boundary incompressible viscous MHD
    Journal of Differential Equations, 379: 26–103, 2024.
  4. Jie Fu, Chengchun Hao, Siqi Yang and Wei Zhang;
    A Beale-Kato-Majda criterion for free boundary incompressible ideal magnetohydrodynamics
    Journal of Mathematical Physics, 64(9): 091505 (16pp), 2023.
  5. Chengchun Hao and Wei Zhang;
    A priori estimates for free boundary problem of 3D incompressible inviscid rotating Boussinesq equations
    Zeitschrift für angewandte Mathematik und Physik, 74(2): 80 (21pp), 2023.
  6. Chengchun Hao and Tao Luo;
    Some results on free boundary problems of incompressible ideal magnetohydrodynamics equations
    Electronic Research Archive, 30(2): 404-424, 2022.
  7. Chengchun Hao and Tao Luo;
    Well-posedness for the linearized free boundary problem of incompressible ideal magnetohydrodynamics equations
    Journal of Differential Equations, 299: 542-601, 2021.
  8. Chengchun Hao and Tao Luo;
    Ill-posedness of free boundary problem of the incompressible ideal MHD
    Communications in Mathematical Physics, 376(1): 259–286, 2020.
  9. Chengchun Hao;
    On the motion of free interface in ideal incompressible MHD
    Archive for Rational Mechanics and Analysis, 224(2): 515–553, 2017.
  10. Chengchun Hao and Tao Luo;
    A priori estimates for free boundary problem of incompressible inviscid magnetohydrodynamic flows
    Archive for Rational Mechanics and Analysis, 212(3): 805-847, 2014.

  11. ♣ Two-phase equations
  12. Chengchun Hao, Tao Luo and Siqi Yang;
    Exponential stability of a free boundary problem with spherical symmetry for a gas bubble immersed in a bounded incompressible liquid NEW
    Accepted by Calculus of Variations and Partial Differential Equations, 2025.
  13. Wei Zhang, Jie Fu, Chengchun Hao and Siqi Yang;
    Global well-posedness for two-phase fluid motion in the Oberbeck-Boussinesq approximation
    Journal of Mathematical Physics, 65(8): 081509 (22pp), 2024.
  14. Chengchun Hao and Wei Zhang;
    Local well-posedness for two-phase fluid motion in the Oberbeck-Boussinesq approximation
    Communications on Pure and Applied Analysis, 22(7): 2099-2131, 2023.
  15. Chengchun Hao and Wei Zhang;
    Maximal $ L^p$-$ L^q$ regularity for two-phase fluid motion in the linearized Oberbeck-Boussinesq approximation
    Journal of Differential Equations, 322: 101-134, 2022.

  16. ♣ Elastodynamics
  17. Fu Jie, Hao Chengchun*, Yang Siqi, Zhang Wei;
    A blow-up criterion for free boundary problem of incompressible neo-Hookean elastodynamics
    SCIENTIA SINICA Mathematica, 55: 1–16, 2025.
  18. Hao Chengchun*, Wang Dehua;
    A priori estimates for the free boundary problem of incompressible neo-Hookean elastodynamics
    Journal of Differential Equations  261(1), 712–737, 2016.    

  19. ♣ Euler equations
  20. Chengchun Hao;
    Remarks on the free boundary problem of compressible Euler equations in physical vacuum with general initial densities
    Discrete and Continuous Dynamical Systems - B, 20(9): 2885-2931, 2015.

  21. ■ Well-posedness of Cauchy problems to fluid dynamics equations

  22. Chengchun Hao and Hai-Liang Li;
    Well-posedness for a multidimensional viscous liquid-gas two-phase flow model
    SIAM J. Math. Anal., 44(3): 1304–1332, 2012.
  23. Chengchun Hao;
    Global well-posedness for a multidimensional chemotaxis model in critical Besov spaces
    Zeitschrift für angewandte Mathematik und Physik, 63(5): 825-834, 2012.
  24. Yiquan Lin, Chengchun Hao and Hai-Liang Li;
    Global well-posedness of compressible bipolar Navier-Stokes-Poisson equations
    Acta Mathematica Sinica, English Series, 28(5): 925-940, 2012.
  25. Chengchun Hao;
    Well-posedness for the viscous rotating shallow water equations with friction terms
    J. Math. Phys., 52(2): No.023101, 12pp, 2011.
  26. Chengchun Hao;
    Well-posedness to the compressible viscous magnetohydrodynamic system
    Nonlinear Analysis: Real World Applications, 12(6): 2962–2972, 2011.
  27. Chengchun Hao;
    Cauchy problem for viscous shallow water equations with surface tension
    Discrete Contin. Dyn. Syst. Ser. B, 13(3): 593-608, 2010.
    We are concerned with the Cauchy problem for a viscous shallow water system with a third-order surface-tension term. The global existence and uniqueness of the solution in the space of Besov type is shown for the initial data close to a constant equilibrium state away from the vacuum by using the Friedrich's regularization and compactness arguments.
  28. Chengchun Hao, Ling Hsiao and Hai-Liang Li;
    Cauchy problem for viscous rotating shallow water equations
    Journal of Differential Equations, 247(12): 3234–3257, 2009.
  29. Chengchun Hao and Hai-Liang Li;
    Global existence for compressible Navier–Stokes–Poisson equations in three and higher dimensions
    Journal of Differential Equations, 246(12): 4791–4812, 2009.

  30. ■ Well-posedness of IVP/IBVP to dispersive equations

  31. Recent progress on some kinds of nonlinear dispersive partial differential equations (in Chinese)
    Research Series for Excellent Doctoral Dissertation of Chinese Academy of Sciences vol. 2007, 1-6, Science Press, Beijing, 2008.
  32. Chengchun Hao, Ling Hsiao and Hai-Liang Li;
    Global well posedness for the Gross–Pitaevskii equation with an angular momentum rotational term
    Math. Methods Appl. Sci., 31(6): 655-664, 2008.
  33. Chengchun Hao, Ling Hsiao and Hai-Liang Li;
    Global well posedness for the Gross-Pitaevskii equation with an angular momentum rotational term in three dimensions
    J. Math. Phys., 48(10): No.102105, 11pp, 2007.
  34. Chengchun Hao;
    Well-posedness for one-dimensional derivative nonlinear Schr\"odinger equations
    Commun. Pure Appl. Anal., 6(4): 997-1021, 2007.
  35. Chengchun Hao, Ling Hsiao and Baoxiang Wang;
    Well-posedness of Cauchy problem for the fourth order nonlinear Schr\"odinger equations in multi-dimensional spaces
    Journal of Mathematical Analysis and Applications, 328(1): 58-83, 2007.
  36. Chengchun Hao, Ling Hsiao and Baoxiang Wang;
    Wellposedness for the fourth order nonlinear Schr\"odinger equations
    Journal of Mathematical Analysis and Applications, 320(1): 246-265, 2006.
  37. Baoxiang Wang, Chengchun Hao and Henryk Hudzik;
    Energy scattering theory for the nonlinear Schr\"odinger equations with exponential growth in lower spatial dimensions
    Journal of Differential Equations, 228(1): 311-338, 2006.
  38. Chengchun Hao;
    The initial boundary value problem for quasi-linear Schr\"odinger-Poisson equations
    Acta Math. Sci. Ser. B Engl. Ed., 26(1): 115-124, 2006.
  39. Chengchun Hao and Ling Hsiao;
    Studies on Schr\"odinger-Poisson systems (Excerpt of Dissertation)
    J. Grad. Sch. of CAS, 22(5): 141-146, 2005.
  40. Chengchun Hao and Hai-Liang Li;
    On the initial value problem for the bipolar Schr\"odinger-Poisson systems
    J. Partial Diff. Eqns., 17(3): 283-288, 2004.
  41. Chengchun Hao, Ling Hsiao and Hai-Liang Li;
    Modified scattering for bipolar nonlinear Schr\"odinger-Poisson equations
    Math. Models Methods Appl. Sci., 14(10): 1481-1494, 2004.
  42. Chengchun Hao and Ling Hsiao;
    Large time behavior and global existence of solution to the bipolar defocusing nonlinear Schr\"odinger-Poisson system
    Quart. Appl. Math., 62(4): 701-710, 2004.
  43. Chengchun Hao;
    Energy scattering for the generalized Davey-Stewartson equations
    Acta. Math. Appl. Sinica, 19(2): 333-340, 2003.
  44. Energy scattering for nonlinear Davey-Stewartson equations (in Chinese)
    J. Math. Res. Expo. 23(4), 645-650, 2003.   
  45. Energy scattering for the generalized Davey-Stewartson equations (Rapid Communications)
    Hebei Uni., Rat. Sci. Edt. 22(1), 73-74, 2002.

  46. ■ Well-posedness or asymptotic of IVP/IBVP to quantum models

  47. Hai-Liang Li, Guo-Jing Zhang, Min Zhang and Chengchun Hao;
    Long-time self-similar asymptotic of the macroscopic quantum models
    J. Math. Phys., 49(7): No.073503, 14pp, 2008.
  48. Chengchun Hao, Yueling Jia and Hai-Liang Li;
    Quantum Euler-Poisson system: local existence of solutions
    J. Partial Diff. Eqns., 16(4): 306-320, 2003.

  49. Published Books

    已出版著作

    1. Baoxiang Wang, Zhaohui Huo, Chengchun Hao and Zihua Guo;
      Harmonic Analysis Method for Nonlinear Evolution Equations,I
      World Scientific Pub Co Inc 300pp, 2011.   
      [中文版: 非线性发展方程的调和分析方法(I)适定性理论 (未出版, 2010) 下载]